Back-and-forth for systems of antichains
type: Item
instance of: scholarly article
title: Back-and-forth for systems of antichains
zbMATH Open document ID: 0838.03030
DOI: 10.1007/BF01111742
published in: Order
publication date: 1995-12-20T00:00:00Z
review text: The author deals with root systems, that means with partially ordered sets such that the final section of any element is totally ordered. He considers the distributive lattice of all antichains. It is shown that the first-order theory of this distributive lattice is completely determined by the first-order theory of the root system. This is shown by describing a suitable back-and-forth system.
reviewed by: Martin Weese
Mathematics Subject Classification ID: 03C10
Mathematics Subject Classification ID: 06D99
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 03C07
zbMATH DE Number: 828180
zbMATH Keywords: elementary equivalence
zbMATH Keywords: root systems
zbMATH Keywords: distributive lattice
zbMATH Keywords: antichains
zbMATH Keywords: first-order theory
zbMATH Keywords: back-and-forth system
author: Daniel Gluschankof
MaRDI profile type: Publication
cites work: Lex-subgroups of lattice-ordered groups
cites work: The Hahn Embedding Theorem for Abelian Lattice-Ordered Groups
cites work: Q3220545
cites work: Théories d'arbres
cites work: Ordering the set of antichains of an ordered set
cites work: Arborescent Structures. II: Interpretability in the Theory of Trees
cites work: Classification theory and the number of non-isomorphic models
description: scientific article; zbMATH DE number 828180